Question

Line k's equation is y = 2/3x-1 Line l is perpendicular to line k and passes through the point (-1, 5/2) Find an equation for line l in both point-slope form and slope-intercept form. An equation for l in point-slope form is:An equation for l in slope-intercept form is:

Answer 1

The given line k having equation is:

`y=(2)/(3)x-1`

The slope is 2/3.

And the line I is perpendicular to line k, so the slope of line I is:

`\begin{gathered} m_I=-(1)/(m_k) \\ m_I=-(1)/((2)/(3)) \\ m_I=-(3)/(2) \end{gathered}`

So slope of line I is -3/2

An equation for l in point-slope form is:

As it is passing through: (-1, 5/2)

`\begin{gathered} (y-(5)/(2))=-(3)/(2)(x-(-1)) \\ (y-(5)/(2))=-(3)/(2)(x+1) \end{gathered}`

An equation for l in slope-intercept form is:​

`\begin{gathered} (y-(5)/(2))=-(3)/(2)(x+1) \\ y-(5)/(2)=-(3)/(2)x-(3)/(2) \\ y=-(3)/(2)x+(5)/(2)-(3)/(2) \\ y=-(3)/(2)x+((5-3))/(2) \\ y=-(3)/(2)x+(2)/(2) \\ y=-(3)/(2)x+1 \end{gathered}`